If x is an integer, then is x a prime number?

(1) x is a multiple of a prime number.
(2) x is a product of two integers.

let me just further elaborate on Bunuel
(1) let the prime number be 2 then 2*1= 2 this is a prime number
again 2*2 =4 this is not a prime number so both 2 and 4 are multiples of the prime number 2, but 2 is a prime number and 4 is not so (1) is not sufficient


similarly 6 is a product of 2 integers 3*2 and 6 is not a prime number
but 2 is also a multiple of 2 integers 1*2 and 2 is a prime number
so (2) is also not sufficient

Taking both (1) and (2)
First number 2 , (1) Is a multiple of a prime no.( 2*1)
(2) is the product of 2 integers (2*1)
and 2 is a prime number

second number 6, (1) Is a multiple of a prime no.( 3*2)
(2) is the product of 2 integers (3*2)

and 6 is not a prime number

as both 1 and 2 together do not give a consistent answer the answer is e

Hope I have understood it correctly ,

Thanks Bunuel

x is a multiple of a prime number --> x = prime*k = 2*1.
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Question is - is X a prime number? We can get two amswer - either Yes - x is PN or No-x is not PN. For me, both would be correct.

When we solve statement 1 and 2, each statement's answer shows that X is not a Prime # i.e. each statement provides an answer

However the answer is only emphasis on Yes answer. Since we do not get the Yes anwer from both statements, both are not sufficient. Why is that? Is this how we are supposed to think in DS problems